The one thing I would worry about the most is probably tape worms. My husband is an avid hunter, and when he would bring home rabbit's from the day's hunt...I would not let him bring them in the house to skin and clean because the pelts were alway's full of flea's.
Tape worms are passed on to a dog or cat by ingesting flea's. Your little hunter could have swallowed a few flea's while mouthing his prize.